Inductive device having a precisely sinusoidal relation between coupling and relative displacement



P. F. BECHB-ERGER ET AL May 1, 1951 2,550,663

INDUCTIVE DEVICE HAVING A PRECISELY SINUSOIDAL RELATION BETWEEN COUPLING AND RELATIVE DISPLACEMENT 2 Sheets-Shef. i

Original Filed March 27, 1947 WINDING DISTRIBUTIONS SLOT PITCH 0 OF TOTAL TURNS SE m R UA E H Tm D m mm r... Y m m m m hm m aumw m 0 m Y w I U E m w I 3 P 432 m T m w A $5 9 mun "in mwm mmw 22 l\ 73o NORMAL WINDING SPLIT AND OF LADDER-TYPE ONE OF THREE, SHOWN 5 mm y M54 6 m W m we m a Mam F5 0 L UN n MP" May 1, 1951 P F BECHBERGER ET'AL 2,550,663

INDUCTIVE DEvIcE HAVING A PRECISELY SINUSOIDAL RELATION BETWEEN COUPLING AND RELATIVE DISPLACEMENT Original Filed March 27, 1947 2 Sheets-Sheet 2 WINDINGS AS IN FIG. I

OF TOTAL 7 I A TURNS PER PHASE NUbUIQfl 1.01 3,Y CONNECTED (l 9! SHOWN) ALTERNKTIVELY, NDIM MAY BE EITl-ER SINGLE-PHA$E T -PHA$E WITH NORMAL WINDING SPLIT AND LADDEFb-TYPE INVENTORJ" PHUL F. BEL'HBEREER PHNUSE. YEHNNHK IE Patented May 1, 1951 INDUCTIVE. DEVICE-HAVIN G A PnEoIsELY SINUSOIDAL RELATION BETWEEN COU- PI I N'G, RELATI Paul F. BechbergenTenafly, and-Banos G.

nakis, Maplew i' N- v at on Corrt on, e eti nf D aw re Continuation of application Serial Mai-ch 27, 1947; application 1949,.Sei-ialNo. 121 316 (o1. sis- 24) Ijhepresent-inyention relates to induction devices-having relativelymovabl parts and, more particularly, to synchros commonly used telemetrically with alternating current energization, and is a continuation in whole of the invention disclosed in our abandoned application Serial No. 737,452 filed March 27, 1947, assigned to the same asslgn e-as the present invention.

The inventign relates especially to novel means y which a p ec sely sinus i a i niso tained, with a consequent mprovement in teleetri c ura y- This. invention constitutes an improvement over the invention disclosed -i,-nco- -pending application Serial No. 550,461., filed August 21, 1944, by John P. Glass, Jr., now Patent No. 2,488,771, dated November 2;, i949, assi ned to the assignee of the present invention, in thatthe lowest-order 'uncancelled harmonic is of at least twice the order and hence is of considerably smaller possible magnitude because Of the generally inverse relation existing. between the maximum possible magnitude and the order .ofharmonic.

In the most efiicient windings disclosed in said (Glass Patent No. 2,488,771, the 17th and 19th harmonics are the lowest-order pair of uncan celled-harmonics, their resultant e ror appearing :as th 18th for reasons which appear in a recent :article Electrical Accuracy of Selsyn Generator- Control: Transformer System" by Harold Chest- :nut, American Institute of Electrical Engineers Transactions, August-September 1946, volume 65, ;pages 570-576, on page 573 of which a 6th order error is shown to result from uncancelled th :and 7th harmonics.

By zone of the embodiments of the present in- '-.vention, the 35th and 37th harmonics are the llowest orders uncancelled, with a consequent :generally negligible error of the 36th harmonic.

In another embodiment of the present invention, the 59th and 61st harmonics are the lowest orders uncancelled, with a consequent still small- :er possible error of the 60th harmonic.

Accordingly, one-of the objects Ofthe present finvention is to provide novel and improved induction devices having a higher order-of accuracy than was heretofore obtainable.

Another object is to provide novel and improved synchros, whereby the accuracy of telemetric transmission synchro systems is greatly :improved by distributing the windings of both the rotor and the stator of each synchro unit in accordance-with the distribution obtained by ap-- plying the method disclosed in said Glass Patent VB PIPSP-PAQEMENT Yean- 1., assignorsfto, Bendix, T terbora; N. a. c n

No. 737,452, October '14,

ings' are for the p rpes of illustrationand' description only and are not intended as a defi'iil' f tion or the'lin its of the invention; reference being ha'gl'to' the appended claims for this purpose.

In, "t e drawings wherein lilie refereneefcharactors refer to like parts throughout the views;

Fig. 1 is a front elevation of one embodiment of the invention, in whicha l2-'sl6t rotdnand a H-slot stator respectively appear on the lefthand and righthand. sides, a synchro being shown by way of example. This view shows a winding distribution which provides the increased accuracy;

Fig. 2 is a perspective view of the same elements, in the same general relative positions, to show the relative skew and thickness of theseelements; and

Fig. 3 is a view generally similar to Fig. l but showing a 15-51% stator with the same'lZ-slot rotor, a synchro combination of still higher accuracy.

Referring to Figs. 1 and 2, the rotor l is mounted to be angularly movable in stator 2, both being laminated and with 12 and 9 evenly spaced slots, respectively, as shown. Dummy slots (not shown) may, if desired, be used to provide effective slots where hese need not contain coils.

The rotor I is bisymmetrical, i. e., symmetrical about ,two axes 1-1 and II II which are normal to each other and to the axis of -.ro at on. a new salient bipole rotor being shown. This bisyrnmetry, as noted in said Gla s Patent, eliminate all even order harmonics of coupling to angle of relative displacement of rotor to stator.

The .rotor winding 3 is distributed as shown in the. distributionobtained by applying the, method disclosed in the aforesaid Glass Patent No. 2,488,771, namely, in accordance with the 'distributio'n determined by the simultaneous solution of .anumber of equations each of which is equal to zero and represents a to-be-neutralized Fourierharmonic in the relation of the coupling totherelative position orthero'tor and the stator. each of such equations including a finite series of sinusoidal terms expressing, for a respective independent coil and for the particular harmonic, the coupling factor of the coil as dependent upon both the number of its .turns and the efiective positions of its conducting bars at any number of equally spaced points, so that the independent, coils have their bars effectively lumped at electrical angles'which are integer multiples of the spacing between said points. If the stator (orrotor) is provided with an in odd number of slots as, for example, the stator shown in Figs. 1, 2 and 3, then the windingthereon is distributed according to-the simultaneous solution of a plurality of equations of the formula including the pertinent terms in where N is the number of turns in a coil of slot pitch indicated by the subscript, n is the odd number of slots in the stator (or rotor), and h is the order of an appreciable odd harmonic to be suppressed, whereby each of the harmonics thus considered is substantially eliminated to obtain a sinusoidal relation between the angle of relative rotation and the ratio of the input and out: put voltages. I

On the other hand, if the rotorior stator) is 1.. provided with an even number of slots alsgljforl; example, the rotor shown in Figs. 1, 2. anus, then the winding thereon is distributedaccotd ing to the simultaneous solution of ,a..plurality of equations of the formula including theperti: nent terms in 90 N ("4) cos 5h n 20 90 90. N (sis-1 00S a +1} (11- 005 U where N is againthe number of turns in-a coil of slot pitch indicated by the subscript, n is the even number of slots inthe rotor (or stator) and 1:. is the order of an appreciable odd harmonic to be suppressed as in Equation I.

It will thus be seen that Equations I and 11 59 are of identical form, exceptthat Equation I is used when the rotor or stator is provided with an odd number of slots, and Equation 11 is used when the rotor or stator is provided with an even number of slots.

The aforesaid distribution of the rotor winding- 3 directly eliminates all odd -harmonics except the 11th. By symmetry, only the 13th; 23rd and 25th; 35th and 37th: order odd harmonies are not'neutralized. In other words, this rotor eliminates all odd harmonics except those of order A1211, where A is any integer. T

The rotor winding eliminates the 3rd and 17th harmonics. Since the rotor winding eliminates all harmonics divisible by three, this synchro .65 may be used in two-phase, instead of i i-phase, connection with a 9-slot stator without error due to these harmonics even though said stator does not eliminate all of them.

The B-phase, Y-ccnnected windings 4 for the 70 9- 'slot stator are shown distributed as for one form in said Glass patent, Figs. 6 and 20 thereof. Said stator coil distribution relies upon 'the' 3-phase Y-connection and/or'the rotor winding distribution-to eliminate the 3rd harmonic, and (6 4 directly eliminates the 5th and 7th harmonics. By symmetry, the stator eliminates all odd harmonies except the 17th, 19th; 35th, 37th; In other words, this stator eliminates all harmonies except those of orders 318:1, where B is any integer.

Thus, it is evident that the synchro of Figs. 1

q and 2 eliminates all harmonics up to the 35th and 37th orders, with a consequent generally negligible 36th harmonic error of the coupling to angle relation.

'By applying the teachings of the aforesaid Glasspatent in accordance with the present in-- vention, a harmonic may be additionally eliminatedas, e. ,g. by the use of a Y-connection in. the windingof the-rotor, which is shown as.

single-phase in Fig. 1, with a resultant decrease in permissible production tolerances.

Where still higher accuracy is required than isobtainable with the synchro of Figs. 1 and 2, the synchro of Fig. 3 may be used, with the lowest: uncancelled harmonic appearing as an error of the th order.

The sync'hro of Fig. 3 has the 12-sl0t rotor of Figs. 1 and 2 but a' 15-slot stator with the hereinstated winding distribution as in the aforesaid Glass patent, from Fig. 19 thereof and its context therein. With this 15-slot stator, the 3-phase, Y-connected windings are conveniently used, with a consequent double elimination of the 3rd harmonic as for Figs. 1 and 2. e

For the 15-slot stator winding, in 3-phase Y-connection, any phase may be distributed as follows, from said G rlass patent,

magf Per cent of pendent turns coil per phase so that this 15-slct stator directly eliminates all odd harmonics except the 29th, with the 31st; 59th, 61st; eliminated by symmetry.

In combination with the 12-s1ot rotor of the instant application, this 15-slot stator thus has the first coincidence of uncancelled harmonics appear as the 59th and 61st which result in a 60th harmonic error of the coupling-to-angle relation. As earlier brought out herein, thishigher order of the lowest-order 'uncancelled harmonic results in a worthwhile reduction in the magnitude of: the .error.

Although only two embodiments of the invention have been illustrated and described, various changes and modifications in the form and 'rela-' tivearrangement of the parts, which will now be apparent to those skilled in the art,- may be made without departing from the scope of the invention. Reference is, therefore, to be had to the appended claims for a definition of the limits of the invention.

In particular, the use in the claims of "rotor" and stator is for conciseness but these are intended to be used interchangeably, and to have as equivalents linear inductive elements which are relatively movable longitudinally without change ofthel'r distance apart, Likewise one efiectiveslot-"pitch relative skewing" of the inductive elements means thatthe slot-pitch is thatofthez.

ske-Wedelement, e: ga skew of-a 12'-slot-erotor or- 40 skew ofa 9-slot stator whichever is skewed- (preferably therotor only as a matter of mechanical convenience). Throughouttheclaims: the stated harmonics are in the relation of the coupling to the relative angle between rotor and stator, and also a number of equally spacedv slots is. intendedv to include slots" angularly spaced by integer-mulitples of" 360/M, where M is a positive" integer. And substantially, as

applied to the winding'distribution, means that the total number of turns in any coil is: within either oneturn or 2 per cent (based 'on the' total numberof turns), whichever is the larger of the theoreticalvalue.

What is claimed is:

1. In anelectrical device, the combination of two relatively movable inductively coupled elements, each of said elements having a windingdistributed into coils with the number of turns in each independent coil substantially in accordance with the distribution determined by the simultaneous solution-of a'number of equations each of which is equal to zero and represents a to-be-- neutralized Fourier harmonic in the relation of the coupling to the relative position of said two elements, each of said equations including a finite series oflsinusoidal terms, and each of said terms expressing. for a respectiveiindependent coil and for the particular harmonic, the coils coupling factor as dependent uponboth the number of its turns and the efiective positions of its conducting. bars at any of a number of equally spaced points so that the independent coils have their bars effectively lumped atelectrical angles-which are integer multiples-ofthe spacing between said points.

2; In an electrical alternating? current. device having two inductively coupled relatively movable: elements, a winding on each ofsaid elements dis-- tributed to have the average numeroi the conductor bars of said winding per electrical degree vary with the electrical angle'of the bars" from a neutral-coupling reference position over a range of up to 90 electricaldegrees substantially according to the solution of a determinant which, includes a number of equations each or which is equalto zeroand represents a to-be-neutralized harmonic in the relation of the couplingi t'obthe: relative position of said two elements, each of said equations including a finite series of sinusoidal terms, and each of said terms expressing,- for each bar and the particular harmonic,.the barfs coupling factor as dependent upon its electrical angle from the reference position.

3. An electrical alternating;current device having twoinductively coupled relatively movable elements having windings, each of said-' elements being constructed to have an integral number of evenly spaced slots per an integral number times 360 electrical degrees and its winding in a selected number of said slots with a number of'turns of each independent coil of different slot-pitch, the number of turns of each suchcoi'l'being substantially in accordance with the solution-of a determinant which includes a number ofequations' each of which is equal to zero and' represents a to-be-neutralized harmonic in the relation of the coupling to the relative position of said two elements, each of said equations including a finite series of sinusoidal terms, and

each of said terms expressing, for each independent coil and the particular harmonic, the

coil's lcoupiingi factor esdepericlent upondtscslotw:

pitch:

4. An electrical A. 0. devicehaving-prelativelw movable rotor and stator elements, one of said elements including ahselected number or inde pendent coils Wound symmetrically about an axis normal" both tothat of said coils-and to: that of relative rotation upon" a core having: an oddnu'mber of.- equally-spaced slots, substantially according to" the simultaneous solution of a' .pluralit'yyof equations ofitlie formula including; the ertinent:

termsin whereiN is the-number of turnstin a coil of slot pitch indicated by the subscript, n. is the odd number of slots in said core, and his the order! of i an appreciable odd harmonic "to be suppressed,

whereby, each of the harmonics thus considered is substantially eliminated to obtain a sinusoidal.

relation between the angle of said relativeroetation and the ratio of the output and input voltages, the other'of' said elements" including a' selected number of" independent" coils wound symmetrically about'an' axi's'normal'both to that" of i said coils: and to that ofrelative rotationtuponl a core having an even-numberof equallyespacedv.

slots, substantially according, to thesimultaneous solution of a plurality of equations oft? the: for;- m'ula including the pertinentterms in O N (nu-5) gg where N'isthe number of" turns in acoilofslot pitch" indicated bythe subscript, n is the even number of slots insaid core; and h is the order of an appreciable odd harmonieto be suppressed, whereby each of the harmonics thus considered-is substantially eliminated toobtain a sinusoidal relation between the angle of said relative rotation and the ratio of the output and input voltages.

5; An electrical A. C. device, h'aving'rel'atively movable ,rotor and stator elements, said stator element including a selected. number of independent coils wound" symmetrically about an axis normal both to that of said coils and to that of relative rotation upon a core having an odd number of equally-spaced slots, substantiallyaccording to the-simultaneous solution of a plurality of equations of the formula including the-pertinentterms in where N is the number of turns in a. coil of slot pitch indicated by the subscript, "n, in the odd number of slots in said core, and h isthe order of an appreciable odd harmonic to be suppressed, whereby each of the harmonics thus considered is substantially eliminated to obtain a sinusoidal relation between the angle of saidrelative rotation and the ratio. of the output and inputvoltages, saidrotor elementincluding a selected num-- her or independent coils wound symmetrically about an. axis normal both-to that of. said coilsand tothat of relativerotationiupon a-corehavw in: an even'number of equallwspacedslots subassaces stantially according to the simultaneous solution of a plurality of equations of the formula including the pertinent terms in 90 N( /z S h 7 where N is the number of turns in a coil of slot pitch indicated by the subscript, "n is the even number of slots in said core, and h is the order of an appreciable odd harmonic to be suppressed, whereby each of the harmonics thus considered is substantially eliminated to obtain a. sinusoidal relation between the angle of said relative rotation and the ratio of the output and input voltages.

6. An inductive device of the class including synchros, comprising a stator and a rotor relatively movable angularly thereof, said rotor being bisymmetrical nonsaiient bipole, whereby all even harmonics are eliminated, with 12 equally spaced effective slots containing coils with their windings distributed substantially as follows:

Slot pitch 2 4 6 Per cent of total turns 13.45 23.1 26.9 Coils 2 2 i Slot pitch 1 3 Per cent of total turns 6.7 18.3 25.0 Coils 2 2 2 said stator being symmetrical with an integer number C of equally spaced effective slots with coils wound in a selected number of said slots to eliminate most of the otherwise uncancelled odd harmonic content except of orders DCil, where D is an even integer when C is odd and vice versa.

8. An inductive device of the class includin synchros, comprising a stator and a rotor relatively movable angularly thereof, said rotor being bisymmetrical bipole, whereby all even harmonics are eliminated, with an even number A of equally spaced slots some of which contain coils with their windings distributed to eliminate most of the otherwise uncancelled odd harmonic content except of orders BAil, where B is any integer; said stator being symmetrical with 9 evenly spaced eiiective slots containing windings with each phase-winding distributed substantially as follows in unsplit coils:

Slot pitch l 3 2 Per cent of total turns 53.2 34.7 12.1

9. An inductive device of the class including synchros, comprising a stator and a rotor relatively movable angularly thereof, said rotor being bisymmetrical bipole, whereby all even harmonics are eliminated, with an even number A of equally spaced slots some of which contain coils with their windings distributed to eliminate most of 8 the otherwise uncancelled harmonic order cori= tent except of orders BAil, where B is any integer; said stator being symmetrical with 15 evenly spaced effective slots containing 3-phase' windings with each phase-winding distributed substantially as follows in unsplit coils:

Slot pitch '7 6 5 4 3 2 Per cent of total turns 31.6 27.5 20.5 12.7 6.0 1.7

10. An inductive device of the class including synchros, comprising a stator and a rotor, said rotor" being bisymmetrical non-salient bipole, whereby all even harmonics are eliminated, with 12 equally spaced effective slots containing coils with their windings distributed substantially as follows:

Slot pitch 2 4 6 Per cent of total turns 13.45 23.1 26.9 Coils 2 2 1 11. An inductive device of the class including sy-nchros, comprising a stator and a rotor, said .rotor being bisymmetrical non-salient bipole,

whereby all even harmonics are eliminated, with 12 equally spaced effective slots containing coils with their windings distributed substantially as follows:

Slot pitch 2 1 3 5 Per cent of total turns 6.7 18.3 25.0 Coils 2 2 2 said stator being symmetrical with 9 equally spaced effective slots containing B-phase windings with each phase winding distributed substantially as follows:

Slot pitch; 4 3 2 Per cent of total turns 53.2 34.7 12.1

12. An inductive device of the class including synchros, comprising a stator and a rotor, said rotor being bisymmetrical non-salient bipole, whereby all even harmonics are eliminated, with 12 equally spaced effective slots containing coils with their windings distributed substantially as follows:

Slot pitch 2 4 6 Per cent of total turns 13.45 23.1 26.9 Coils 2 2 1 said stator being symmetrical with 9 equally spaced effective slots containing B-phase windings with each phase winding distributed substantially as follows:

Slot pitch 7 6 5 4 3 2 Per cent of total turns 31.6 27.5 20.5 12.7 6.0 1.7

Slot pitch l 3 5 Per cent of total turns 6.7 18.3 25.0 Coils 2 2 2 said stator being symmetrical with 9 equally spaced eflective slots containing S-phase windings with each phase winding distributed substantially as follows:

Slot pitch 7 6 5 4 3 2 Per cent of total turns 31.6 27.5 20.5 12.7 6.0 1.7

14. An electrical A, C. device having relatively rotatable rotor and stator elements, one of said elements including a selected number of independent coils woun i symmetrically about an axis normal both to that of said coils and to that of relative rotation upon a core having an even number of equally-spaced slots, substantially according to the simultaneous solution of a plurality of equations of the formula including the pertinent terms in 90 90 N (1:12-11 00S miw ai 00S g 5+ where N is the number 01' turns in a coil of slot pitch indicated by the subscript, n is the even number of slots in said core, and h is the order of an appreciable odd harmonic to be suppressed. whereby each of the harmonics thus considered is substantially eliminated to obtain a sinusoidal relation between the angle of said relative rotation and the ratio of the output and input voltages.

PAUL F. BECHBERGER. PANOS G. YEANNAKIS.

REFERENCES CITED The following references are of record in the file of this patent:

NrrfiD STATES PA'I'ENTS Name Date Glass, Jr. Nov. 22, 1949 Number 

